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EXPAND sqrt{/frac{1-x}{1+x}}

  • one year ago
  • one year ago

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  1. Calculator
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    \[\Huge \sqrt{\frac{1-x}{1+x}}\]

    • one year ago
  2. Calculator
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    up to power x^2

    • one year ago
  3. Calculator
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    i get \[1-x+\frac{x^2}{2} - \frac{x^3}{8} - \frac{3x^4}{64}\]

    • one year ago
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    @saifoo.khan

    • one year ago
  5. Calculator
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    wolfram got \[-\frac{3 x^5}{8}+\frac{3 x^4}{8}-\frac{x^3}{2}+\frac{x^2}{2}-x+1\]

    • one year ago
  6. saifoo.khan
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    Unfortunately i forgot the formula! D:

    • one year ago
  7. wio
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    Is it a maclaurin series?

    • one year ago
  8. Calculator
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    you can try that

    • one year ago
  9. wio
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    I want to know what is meant by Expand, since that's the only thing that comes to mind.

    • one year ago
  10. Calculator
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    you can use this \[(x+a)^n=\sum ^{n}_{ k=0} \left(\begin{matrix}n \\ k\end{matrix}\right) x^k a^{(n-k)}\]

    • one year ago
  11. Calculator
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    or \[(1+x)^n = 1+nx+\frac{(n)(n-1)}{2!}(x^2)+...\]

    • one year ago
  12. wio
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    That works for \(n\in \mathbb{N}\).

    • one year ago
  13. wio
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    In this case you have a square root...

    • one year ago
  14. Calculator
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    still can, watch

    • one year ago
  15. Calculator
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    \[\sqrt{\frac{1-x}{1+x}} \\ \\ \frac{\sqrt{1-x}}{\sqrt{1+x}} \\ \\ (1-x)^\frac{1}{2}(1+x)^{-\frac{1}{2}}\]

    • one year ago
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    expand separately

    • one year ago
  17. Calculator
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    mix them by multiplying together

    • one year ago
  18. wio
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    Yeah, my problem is with \(1/2 \notin \mathbb{N}\)

    • one year ago
  19. Calculator
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    I don't think it should be natural number

    • one year ago
  20. Calculator
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    i mean real number will do

    • one year ago
  21. wio
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    How can you have summations or binomial coefficients with rational numbers?

    • one year ago
  22. amoodarya
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    interval of x is ?

    • one year ago
  23. Calculator
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    the formula list says can use

    • one year ago
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  24. Calculator
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    we use the second one (1+x)^n

    • one year ago
  25. Calculator
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    http://en.wikipedia.org/wiki/Binomial_series look at the History section

    • one year ago
  26. amoodarya
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    |dw:1359798673882:dw|

    • one year ago
  27. amoodarya
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    |dw:1359798819059:dw|

    • one year ago
  28. Calculator
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    or maybe its \[-\frac{3 x^5}{8}+\frac{3 x^4}{8}-\frac{x^3}{2}+\frac{x^2}{2}-x+1\]

    • one year ago
  29. Calculator
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    hmm

    • one year ago
  30. Calculator
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    based from the formula as long as its in the from ("1"+x)^n should be fine to expand, i tried it

    • one year ago
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    from \[(1-x)^{1/2} \\ \\ n=-1/2, x=-x(for formula) \\ \\ [1-\frac{x}{2}+\frac{(\frac{1}{2})(\frac{1}{2}-1)}{2}(x^2)] \\ \\ 1-\frac{x}{2}-\frac{x^2}{8}\]

    • one year ago
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